How did Gulliver entertain the court with his sailor's skills?none
I'm not sure which court you mean. He "entertained" many courts during his excursions.
If you mean the Lilliputian court, he most likely entertained them with his sailing skills by walking out into the ocean and sinking their opponents' ships (the Blefescu ships represented France). Actually, he refused to sink them as he is a humanitarian, but he did take them by the anchors and walk them back to their own ports...far from where they could do harm to Lilliput.
He entertained the Brobdingnagian court in many ways including a demonstration of gun powder until the King decides that Gulliver's people are "among the most odious vermin to ever crawl upon the face of the earth" based on his stories of corruption, murder, manipulation, lying, etc. There is one section here where he is treated as a "doll" and lives in a dollhouse, "sails" on a doll boat, etc.
He entertains the English court with stories of his visits to these places and more, including the floating island where he tells about his rescue, and how they collect "brain taxes" from earth-bound peoples. He also describes the land of the Houyhnhnms where horses are the logical ones and humans (Yahoos) are beasts.